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The Strict Topology in a Completely Regular Setting: Relations to Topological Measure Theory

Published online by Cambridge University Press:  20 November 2018

Steven E. Mosiman  and
Robert F. Wheeler
Steven E. Mosiman
Affiliation:
University of Missouri, Columbia, Missouri
Robert F. Wheeler
Affiliation:
Louisiana State University, Baton Rouge, Louisiana
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Let X be a locally compact Hausdorff space, and let C*(X) denote the space of real-valued bounded continuous functions on X. An interesting and important property of the strict topology β on C*(X) was proved by Buck [2]: the dual space of (C*(X), β) has a natural representation as the space of bounded regular Borel measures on X.

Now suppose that X is completely regular (all topological spaces are assumed to be Hausdorff in this paper). Again it seems natural to seek locally convex topologies on the space C*(X) whose dual spaces are (via the integration pairing) significant classes of measures.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 5 , October 1972 , pp. 873 - 890
Copyright
Copyright © Canadian Mathematical Society 1972

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